Question

Why does the stream of water from a faucet become narrower as it falls (Fig. 10–43)?

FIGURE 10–43 Question 12. Water coming from a faucet.

Short answer

When the water is away from the faucet, the water velocity is greater and slower near the faucet. So, the cross-sectional area should be narrower when it falls.

Step-by-step solution

Understanding the application of continuity equation in the fluid flow

According to the continuity equation, the incompressible fluid having greater velocity has a lesser cross-sectional area and vice versa. The area of the cross-section and the velocity of the fluid are inversely related to each other.

Explaining the reason behind the stream of water from a faucet becomes narrower as it falls

As the water falls vertically, then the velocity of the water is greater near the surface of the Earth. And its velocity is lesser near the faucet.

The gravity effect is more significant near the surface of the Earth. The stream of water has a higher velocity near-surface of the Earth. Then, the cross-sectional area should be small or narrower.

That is why the stream of water from a faucet becomes narrower as it falls.